General Physics 1 Second Periodic Exam Review

Specific gravity is the ratio of the density of a substance to the density of water. A specific gravity of 0.80 means the substance is 0.80 times as dense as water. Given that the density of water is 1000 kg/m³, the density of the substance can be calculated as 0.80 × 1000 kg/m³, which equals 800 kg/m³. This indicates that the substance is lighter than water, which is consistent with its specific gravity being less than 1.

An object floats when the weight of the water displaced equals the weight of the object. If 75% of the object's volume is submerged, it displaces an amount of water equal to 75% of its volume. Using the formula for density (density = mass/volume), we can express the object's density as the weight of the displaced water divided by its total volume. Since the density of water is 1000 kg/m³, the mass of the displaced water is 0.75 times the object's volume multiplied by 1000 kg/m³, leading to an object's density of 750 kg/m³.

Archimedes' Principle states that an object submerged in a fluid experiences a buoyant force equal to the weight of the fluid that the object displaces. This means that when an object is placed in a fluid, it pushes aside a certain volume of that fluid, and the weight of this displaced fluid creates an upward force on the object. This principle explains why objects float or sink depending on their density relative to the fluid.

Pascal's Principle asserts that when pressure is applied to a confined fluid, it is distributed uniformly in all directions. This means that any change in pressure at one point in the fluid will be felt equally at every other point, regardless of the shape or size of the container. This principle is fundamental in understanding hydraulic systems, where force can be multiplied through the application of pressure to a fluid, demonstrating the efficiency and effectiveness of fluid mechanics in practical applications.

Hydrostatic gauge pressure is calculated using the formula \( P = \rho g h \), where \( P \) is the pressure, \( \rho \) is the fluid density, \( g \) is the acceleration due to gravity, and \( h \) is the depth. For water at a depth of 5 m, substituting the values gives \( P = 1000 \, \text{kg/m}^3 \times 9.8 \, \text{m/s}^2 \times 5 \, \text{m} = 49000 \, \text{Pa} \). Thus, the hydrostatic gauge pressure at this depth is 49000 Pa.

According to Newton's law of universal gravitation, the gravitational force between two objects is inversely proportional to the square of the distance between them. If the distance between the objects doubles, the new distance is twice the original distance. The gravitational force is then reduced by a factor of \(2^2\), which is 4. Therefore, the gravitational force becomes one-fourth of its original value while the masses remain unchanged.

Density is a physical property that quantifies how much mass is contained in a given volume. It is calculated by dividing the mass of an object by its volume, providing insight into how compact or spread out the matter is within that object. This relationship is crucial in various scientific fields, including physics and chemistry, as it helps in understanding the behavior of materials under different conditions and in different states of matter.

Sound intensity decreases with the square of the distance from a source. When the distance triples, the intensity is affected by the square of that factor. Specifically, if the distance increases by a factor of three, the intensity decreases by a factor of \(3^2\), which is 9. Therefore, the new intensity is one-ninth of the original intensity.

When a sound source moves toward a stationary observer, the observed frequency increases due to the Doppler effect. The formula to calculate the observed frequency \( f' \) is given by:

\[ f' = f \left( \frac{v + v_o}{v - v_s} \right) \]

where \( f \) is the source frequency (500 Hz), \( v \) is the speed of sound (340 m/s), \( v_o \) is the observer's speed (0 m/s), and \( v_s \) is the source's speed (20 m/s). Substituting these values into the formula yields an observed frequency of approximately 531 Hz.

The Doppler effect refers to the phenomenon where the frequency of a wave changes due to the relative motion between the source of the wave and the observer. When the source moves toward the observer, the waves are compressed, resulting in a higher frequency (or pitch) being observed. Conversely, when the source moves away, the waves are stretched, leading to a lower observed frequency. This effect is commonly experienced with sound waves, such as when a passing siren changes pitch as it approaches and then recedes from an observer.

When a wave transitions between different media, its frequency remains constant because it is determined by the source of the wave. Changes in medium can alter the wave speed and wavelength, but the frequency is inherently linked to the oscillation rate of the source. This consistency ensures that the energy and information carried by the wave are maintained, regardless of how the wave's speed or wavelength may change in different environments.

Wave speed can be calculated using the formula: wave speed = frequency × wavelength. In this case, the frequency is 12 Hz and the wavelength is 0.50 m. By multiplying these values, we get: 12 Hz × 0.50 m = 6.0 m/s. This indicates how fast the wave travels through a medium, confirming that the wave speed is 6.0 m/s.

Sound waves in air are classified as longitudinal waves because the particles of the medium (air) vibrate parallel to the direction of the wave's propagation. As sound travels, air molecules compress and rarefy, creating areas of high and low pressure. This movement allows sound to transmit energy through the medium, distinguishing it from transverse waves, where particle movement is perpendicular to wave direction. Thus, the nature of particle motion in sound waves in air confirms their classification as longitudinal.

At the equilibrium position of a spring oscillator, the restoring force is zero, meaning the mass experiences no net force acting on it. As a result, the mass moves with maximum speed at this point. When the mass is at maximum displacement, it momentarily stops before reversing direction, resulting in zero speed. Therefore, the equilibrium position is where the kinetic energy is highest, confirming that the speed of the mass is indeed at its maximum there.

In a mass-spring system, the total mechanical energy is proportional to the square of the amplitude of oscillation. This relationship arises from the formula for potential energy stored in the spring, which is given by \(E = \frac{1}{2} k A^2\), where \(k\) is the spring constant and \(A\) is the amplitude. When the amplitude is doubled, the energy becomes \(E' = \frac{1}{2} k (2A)^2 = \frac{1}{2} k (4A^2) = 4E\). Thus, doubling the amplitude increases the total energy by a factor of four.

The period of a mass-spring system can be calculated using the formula \( T = 2\pi\sqrt{\frac{m}{k}} \), where \( T \) is the period, \( m \) is the mass, and \( k \) is the spring constant. Substituting the values \( m = 0.50 \, \text{kg} \) and \( k = 200 \, \text{N/m} \) into the formula gives \( T = 2\pi\sqrt{\frac{0.50}{200}} \). This simplifies to approximately 0.314 seconds, indicating the time it takes for one complete oscillation of the mass-spring system.

In simple harmonic motion, Hooke's Law states that the force exerted by a spring is proportional to the displacement from its equilibrium position, represented by F = −kx. The negative sign indicates that the force acts in the opposite direction to the displacement; when the spring is stretched, it pulls back toward equilibrium, and when compressed, it pushes back outward. This opposing force is essential for restoring the system to its equilibrium position, which is a fundamental characteristic of harmonic motion.

Kepler's Third Law describes the relationship between the orbital period of a planet (T) and the semi-major axis of its orbit (a). Specifically, it states that the square of the orbital period (T²) is directly proportional to the cube of the semi-major axis of the orbit (a³). This means that if you know the distance of a planet from the sun, you can determine how long it takes to complete one orbit, illustrating the harmony of planetary motion in our solar system.

Kepler's Second Law, also known as the Law of Equal Areas, states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means that a planet moves faster when it is closer to the Sun, specifically at perihelion, which is the point in its orbit where it is nearest to the Sun. The gravitational pull is stronger at this point, resulting in increased orbital speed compared to when the planet is farther away at aphelion.

To calculate the weight of an astronaut on the Moon, we use the formula: weight = mass × gravitational acceleration. The mass of the astronaut is 60 kg, and the Moon's gravitational acceleration is 1.62 m/s². Multiplying these values gives: 60 kg × 1.62 m/s² = 97.2 N. This means the astronaut would weigh 97.2 Newtons on the Moon, reflecting the lower gravitational force compared to Earth.